[FOM] Historical queries

[joeshipman@aol.com]

Please excuse the typo below, of course I meant to refer to the 
Fundamental Theorem of *Arithmetic*, not "Algebra"!

-- JS
-----Original Message-----
From: joeshipman at aol.com

For each of the following theorems Xi, I need to know:

1) who first assumed Xi (that is, wrote something which makes no sense
unless they believed Xi to be true even if they did not state it)
2) who first explicitly stated Xi as a known result or conjecture
3) who first wrote a proof of Xi

X1: Fundamental Theorem of Algebra (both existence and uniqueness of
prime factorizations; but since existence is so easy, I will accept a
statement of uniqueness; the important question is who first recognized
that there is something that needs proving here)

X2: Irrationality of all square roots of integers that are not perfect
squares (also, if anyone stated this for some infinite set of
non-squares, such as "square roots of primes are irrational", I want to
know this, because the theorem is easier to prove for primes than in
general)

X3: Irrationality of all kth roots of integers that are not perfect kth
powers, for all integers k>1 (or, again, if this was ever stated for
some infinite subset, such as "the kth root of 2 is irrational for all
k").

--JS

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